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olganol [36]
2 years ago
8

I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures

of angles L and J?

Mathematics
1 answer:
Basile [38]2 years ago
5 0

Answer:

m\angle L = 100^{\circ}.

m\angle J = 80^{\circ}.

m\angle M = 100^{\circ}.

Step-by-step explanation:

Since segment JM is parallel to segment KL, quadrilateral JKLM is a trapezoid.

Segment JK and segment LM (the two legs of this trapezoid) are equal in length. Hence, trapezoid JKLM would be an isoscele trapezoid. By symmetry, m\angle L = m \angle K = 100^{\circ}.

Line JK traverses line JM and line KL. \angle J and \angle K are a pair of consecutive interior angles as they are both between JM\! and KL\! and are on the same side of the traversal, JK\!.

Since line JM is parallel to line KL, any pair of consecutive interior angles between these two lines would add up to 180^{\circ} (supplementary angles.) Thus, \angle J and \angle K are supplementary angles; m\angle J + m\angle K = 180^{\circ}.

Since m\angle K = 100^{\circ}, m\angle J = 180^{\circ} - m\angle K = 180^{\circ} - 100^{\circ} = 80^{\circ}.

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